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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

MARK SCHEME for the November 2005 question paper

0580/0581 MATHEMATICS

0580/04, 0581/04 Paper 4 (Extended), maximum raw mark 130

This mark scheme is published as an aid to teachers and students, to indicate therequirements of the examination. It shows the basis on which Examiners were initiallyinstructed to award marks. It does not indicate the details of the discussions that took place atan Examiners meeting before marking began. Any substantial changes to the mark schemethat arose from these discussions will be recorded in the published Report on the Examination.

All Examiners are instructed that alternative correct answers and unexpected approaches incandidates scripts must be given marks that fairly reflect the relevant knowledge and skillsdemonstrated.

Mark schemes must be read in conjunction with the question papers and the Report on theExamination.

CIE will not enter into discussion or correspondence in connection with these markschemes.

The minimum marks in these components needed for various grades were previouslypublished with these mark schemes, but are now instead included in the Report on the

Examination for this session.

CIE is publishing the mark schemes for the November 2005 question papers for most IGCSEand GCE Advanced Level and Advanced Subsidiary Level syllabuses and some OrdinaryLevel syllabuses.

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TYPES OF MARK

Most of the marks (those without prefixes, and B marks) are given for accurate results,drawings or statements.

M marks are given for a correct method.

B marks are given for a correct statement or step.

A marks are given for an accurate answer following a correct method.

ABBREVIATIONS

a.r.t. Anything rounding tob.o.d. Benefit of the doubt has been given to the candidatec.a.o. Correct answeronly (i.e. no follow through)e.e.o. Each error or omissionf.t Follow throughi.s.w. Ignore subsequent workingo.e. Or equivalentSC Special cases.o.i. Seen or implied

ww Without workingwww Without wrong working Work followed through after an error: no further error made

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Page 1 Mark Scheme Syllabus Paper

IGCSE NOVEMBER 2005 0580/0581 4

University of Cambridge International Examinations 2005

1 (a) 1216 B1

(b) 1.47 B1

(c)100

5.11

75.95.11

M1

15.2 A1 ww2 SC1 for 17.9

(d) 74347 o.e. M1

621 A1 ww2

(e) 9.04347 o.e. M1

4830 A1 ww2

(f)(i)

25.3

2350o.e.

M1 Must deal with the minutes correctly

723 to 723.1 A1 ww2

(ii) 200.9 to 201 A1ft their(i) 3.6 r.o.t. to 3sf or better

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2 (a) Correct Scales S1 Accuracy 2 mm throughout question. From8 to 8 forxand ypossible.

(b) Correct triangle ABC T1

(c) (i) Correct translation with vertices at(5, 7), (8, 7), (8, 5)

TR2ft SC1ft for any translation

(ii) Correct reflection with vertices at(4, 2), (7, 2), (7, 4)

FR2ft SC1ft for two points correct or reflection inx= 1 ory= 1

(iii) Correct rotation with vertices at(2, 2), (5, 2), (5, 4)

RN2ft SC1ft for 2 points correct

(d) (i) Correct image drawn with vertices at(3, 2), (7.5, 2), (7.5, 4)

B3 B2 for 3 correct points shown in working. B1for 2 correct vertices s.o.i.

(ii)

5.10

01

15

1

o.e.B2

SC1 for 5.1

1

or

5.10

01

(iii) Stretch

y-axis invariant o.e.

factor3

2

B1

B1

B1

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3 (a) (i) 60 B1

(ii) ( ) 60cos1572157 222 +=RS M2 M1 if one error in formula

13 A2 A1 for

( )169

2=RS www4

(b) (i) 145 B1

(ii)

14

55sin

15

sin=

Qo.e.

M1

14

55sin15sin =Q

M1 Implies previous method

61.4 A1 www3

(iii) (R=) 63.6 B1

( )55sin

'6.63sin'14=PQ M1 their sin(180 55 b(ii)). Could be explicit

equivalent cosine rule

15.3 A1 www3

(c) 55sin'.3.15.'15.2

1'60sin'15.72

1 + M2 M1 for one correct triangle area in working(45.466 + 93.998)

139 or 140 www A2 A1 for 139.4 to 139.5 www4

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4 (a) (i) 12 B1

(ii) 3 B1

(iii) 21 B1

(iv) 2 B1

(v)24

14 o.e B1 Accept probabilities as fractions/decimals/%

(vi)19

12 o.e. B1

(b) (i)21

1122

12 M1

462132 o.e. (0.286) A1 2/7 in simplest form www2

(ii)21

1222

10 M1

their 221

1222

10 o.e. M1

462240 o.e.(0.519) A1 40/77 in simplest form www3

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5 (a) 0.9 or better B1 (0.8888..)

10.1 or better B1 10.1111..)

(b) (i) Correct scales S1 3 to 3 forx, and 11 to 2 forypossible

(ii) 12 points correctly plotted P3ft P2ft for 10 or 11 correct (acc. is 1 mm)

P1ft for 8 or 9 correct

both branches with correct shape C1ft Acc.21 small square, correct shape, not ruled

Graph does not cross the y-axis B1

(c) Any integer[ 1 B1

(d) Correct ruled line from 3 to +3 B2 SC1 for line with gradient of 2 or passingthrough (0, 5) but not y= 5.

(e) (i) 0.45 to 0.3 B10.4 to 0.49 B1

2.9 to 2.99 B1

(ii) x2 1 = 2x3 5x2 M1 i.e. correct multiplication to remove fraction

2x3 6x2 + 1 = 0 A1 www2

(f) (i) Tangent drawn with gradient 2 B1 Parallel by eye to y= 2x 5

(ii) Linear eqn. inxand ywith gradient 2 B1

c = their intercept B1 within 1 mm, dep on linear eqn inxand y

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6 (a) 2 B1

(b) 35631

o.e. M1

30 A1

(c) Isos. triangle or invtan (3

3 o.e. M1

45 A1 www2

(d) ( ) 22 56 +=BD o.e. M1

BDBF21

= M1 Dep. (BF = 3.905.)

angle = invtanBFtheir

3

M1 Dep on previous method

37.5 to 37.54 A1 www4

(e) (l2) = 32 + (their FB)2 o.e. M1 Not for FB = 3

4.92 to 4.93 A1 ww2

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7 (a) (i) ( ) 351.15.22

1 + o.e. M1

63 A1

(ii) their(a) x 24 M1

1512 A1ft

(iii) 1512000 B1ft their(a)(ii) x 1000

(b) (i) 35.03 x 24 x 2.25 M1

1891.62 A1 www2

(ii) 1900 B1ft theirb(i) rounded to nearest 100

(c) (i) 145.12 2 M1

6870 or better A1 (6872.2339 or 6873.125 ( = 3.142))

(ii) [their(a)(ii) their(c)(i)] M1

x 1 000 000 A1 o.e. e.g. using litres

(60 x 60 x 24) M1 Implied by 2.54

2 days 13 hours A1 www4

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8 (a) (i)x

40 B1

(ii)1

40

2

40=

+ xx

o.e.M2

SC1 for2

40

+x

seen

40x= 40(x+ 2) x(x+ 2) o.e. M1 Correctly removes the fraction

40x= 40x+ 80 x2 2x

x2 + 2x 80 = 0 E1 Correct conclusion no errors

(iii) 10 B1

8 B1

(iv) 8 B1ft their positivexdep on one of each sign

(b) (i) m = n + 2.55 o.e. B1

2m = 5n o.e. B1

(ii) 2(n + 2.55) = 5n M1 f.t. their linear equations in n and many correct method to an equation in onevariable

m = 4.25 A1

n = 1.7 A1

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9 (a) 160 < hY 170 B1

(b) (i) Mid values 125, 135, 145, 155, 165, 175,185, 195

M1 Allow 1 slip

(15 x 125 + 24 x 135 + 36 x 145 + 45x 155 + 50 x 165 + 43 x 175 + 37 x 185+ 20 x 195)

M1 Dep on mid values 0.5, allow 1 slip in mid-values (43830)

270 M1 Dep on previous method

162 or better A1 (162.333..) www4

(ii) Mid-values are an estimate of eachinterval o.e.

B1 e.g. exact values not given

(c) p = 15, q = 39, r= 75 B2 B1 for 2 correct.If no labels, take in order given

(d) Correct scales S1

9 points correctly plotted ft P3ft P2ft for 7 or 8 correct acc. 1 mmP1ft for 5 or 6 correct

Curve or line through 9 points C1ft Dep on S shape within21 small square of

points

(e) (i) 162 to 164 B1

(ii) 176 to 178 B1

(iii) 28 to 30 B1

(iv) 167.5 to 168.5 B1

(f) Uses 240 or 241 on cumul, freq. axis M1 e.g. annotates graph or shows values inworking

186.5 to 188 A1 ww2

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U i it f C b id I t ti l E i ti 2005

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